CN111693915A - Functional magnetic resonance complexity measuring method based on multi-scale permutation fuzzy entropy - Google Patents

Functional magnetic resonance complexity measuring method based on multi-scale permutation fuzzy entropy Download PDF

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CN111693915A
CN111693915A CN202010507671.2A CN202010507671A CN111693915A CN 111693915 A CN111693915 A CN 111693915A CN 202010507671 A CN202010507671 A CN 202010507671A CN 111693915 A CN111693915 A CN 111693915A
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王彬
牛焱
孙婕
崔晓红
相洁
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Taiyuan University of Technology
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Abstract

The invention relates to the technical field of signal processing, in particular to a functional magnetic resonance complexity measuring method, namely a multi-scale arrangement fuzzy entropy. The invention solves the problems that the traditional complexity measurement method can not prevent aliasing, has larger difference on high scale, weak noise resistance and poor stability. A functional magnetic resonance complexity measure method-multi-scale permutation fuzzy entropy is realized by adopting the following steps: step S1: preprocessing functional magnetic resonance data; step S2: low-pass filtering; step S3: time series down-sampling; step S4: the time sequence is symbolized; step S5: performing phase space reconstruction; step S6: adopting a fuzzy membership function; step S7: calculating multi-scale permutation fuzzy entropy; the method reduces the aliasing phenomenon of the time sequence during the down-sampling, reduces the variance value on a high scale, and has better noise resistance and stability. The method is suitable for the complexity analysis of the functional magnetic resonance image data.

Description

Functional magnetic resonance complexity measuring method based on multi-scale permutation fuzzy entropy
Technical Field
The invention relates to the technical field of signal processing, in particular to a method for calculating multi-scale permutation fuzzy entropy.
Background
The functional magnetic resonance imaging (fMRI) technology can effectively detect the activation of different functional areas in the cerebral cortex, and is one of the most effective means in the scientific research of brain and cognition. However, under the condition of lower magnetic field intensity, the variation of fMRI signal is weak, and the signal-to-noise ratio of the acquired image data is low due to unavoidable physiological noise and device noise during data acquisition. Therefore, accurate and reliable detection of physiological signals from image data with low signal-to-noise ratio is a primary solution in fMRI-based brain and cognitive science research.
The traditional complexity analysis method is limited by the principle of the traditional complexity analysis method, and the limitation of methodology exists generally. For example: aliasing phenomenon occurring when a time series is down-sampled cannot be prevented; under a high scale, along with the reduction of data time points, the variance of the entropy value increases very fast, and the reliability is reduced due to large variance; the sensitivity to noise is high; thus resulting in inaccurate complexity calculations. Based on this, it is necessary to invent a completely new functional magnetic resonance complexity measure method to solve the above problems. The invention provides a multi-scale permutation fuzzy entropy (mPFEN), which reduces aliasing phenomenon by improving a filter, reduces variance value on a high scale by redefining a down-sampling process, improves anti-noise capability by introducing a sequencing symbolization thought, and is applied to complexity analysis of functional magnetic resonance image data.
Disclosure of Invention
Aiming at the defects and perfection of the existing fMRI signal complexity stability measuring method, the method provides a complexity measuring method which reflects multiple scales, has high signal-to-noise ratio and high stability.
The invention is realized by adopting the following technical scheme:
a functional magnetic resonance complexity measurement method based on multi-scale permutation fuzzy entropy is realized by adopting the following steps:
step S1: and preprocessing the resting state functional magnetic resonance image data.
Step S2: the data is low-pass filtered using a Butterworth low-pass filter (low-pass Butterworth filter).
Step S3: performing data downsampling to average time series in overlapping window with length s to construct continuous coarse-grained time series
Figure RE-GDA0002610664430000021
Step S4: the coarse-grained time series were serialized: and reconstructing the time sequence to obtain new matrixes, and arranging the components in each new matrix according to the ascending order.
Step S5: and performing phase space reconstruction.
Step S6: using fuzzy membership functions
Figure RE-GDA0002610664430000022
Redefining
Figure RE-GDA0002610664430000023
And
Figure RE-GDA0002610664430000024
distance between, is recorded as
Figure RE-GDA0002610664430000025
Step S7: and calculating a multi-scale permutation fuzzy entropy value.
Compared with the traditional functional magnetic resonance complexity analysis method, the functional magnetic resonance complexity measurement method-multi-scale arrangement fuzzy entropy through improving the filter, redefining the down-sampling process, introducing the ordering symbolization idea to improve the traditional method, reflecting the complexity change under different scales, and improving the anti-noise performance and stability of the complexity method.
Description of the drawings:
FIG. 1 is a flow chart of the multi-scale permutation fuzzy entropy algorithm of the present invention;
FIG. 2 is a graph of the variation of fuzzy entropy in multi-scale permutation of simulated original data and data with 20% and 40% noise added and a graph of variation of statistical p-value;
FIG. 3 is a radar plot of rank ambiguity entropy re-confidence in the present invention on scale 1-5;
detailed description of the preferred embodiments
Examples
As shown in fig. 1, the method for measuring the complexity of functional magnetic resonance based on multi-scale permutation fuzzy entropy is implemented by the following steps:
step S1: and preprocessing the resting state functional magnetic resonance image data.
Step S2: the data is low-pass filtered using a Butterworth low-pass filter (low-pass Butterworth filter).
Step S3: performing data downsampling to average time series in overlapping window with length s to construct continuous coarse-grained time series
Figure RE-GDA0002610664430000026
Step S4: the coarse-grained time series were serialized: and reconstructing the time sequence to obtain new matrixes, and arranging the components in each new matrix according to the ascending order.
Step S5: and performing phase space reconstruction.
Step S6: using fuzzy membership functions
Figure RE-GDA0002610664430000027
Redefining
Figure RE-GDA0002610664430000028
And
Figure RE-GDA0002610664430000029
distance between, is recorded as
Figure RE-GDA0002610664430000031
Step S7: and calculating a multi-scale permutation fuzzy entropy value.
In step S1, the preprocessing is performed using spm 8 and dparsf. And correcting a time layer, correcting head movement, normalizing a functional image space into a Montreal nerve research institute (MNI) template, and performing linear trend removal and time domain band-pass filtering.
In step S2, the original fir filter is replaced by a butterworth low-pass digital filter with a relatively flat frequency response having an amplitude of
Figure RE-GDA0002610664430000032
Where t is the filter order, fcIs the cut-off frequency, in this study, t ═ 6 and fc0.5/τ. The advantage of this filter is that it exhibits a flat amplitude in the pass band for its frequency response. In addition, the side lobe is not arranged in the stop band, the rolling speed is high, and the aliasing is reduced.
In step S3, for the original sequence x having the length N, (i) ═ x1,x2,...,xNKth coarse-grained time series of scale factors
Figure RE-GDA0002610664430000033
Is defined as:
Figure RE-GDA0002610664430000034
where s is a scale factor and each time series is of length
Figure RE-GDA0002610664430000035
And s is 1, which is the original time sequence. kth refers to the kth time series generated by overlapping windows. N refers to the original time series length. For example: when s is 2, i.e. the scale is 2, two time series, 1th and 2th respectively, are constructed by overlapping windows, and the two time series are averaged to obtain the final time series.
In step S4, reconstructing the time sequence to obtain a matrix:
Figure RE-GDA0002610664430000036
where τ and pm are the embedding time delay and the permutation dimension, respectively.
Figure RE-GDA0002610664430000037
Each row in the matrix is considered a reconstruction component. Thus, the matrix contains a total of K reconstruction components.
All elements in each reconstruction component are rearranged in ascending order. If the two element values are equal, the next element value of the corresponding reconstruction component is used as the current comparison result, and the current comparison result is rearranged to reflect the instantaneous change trend of the time series. If the next element value remains equal, its index value is used for the ascending reordering. The different symbol sequences can be obtained by index extraction of all the elements of the component in the original reconstruction matrix, each pm! The symbol sequence corresponds to 1 to pm! To a value of (d). Thus, time series
Figure RE-GDA0002610664430000041
Is converted to have a value between 1 and pm! A completely new sequence of values in between.
Figure RE-GDA0002610664430000042
In step S5, the phase space reconstruction method: assume that the length of U is L.
Figure RE-GDA0002610664430000043
Wherein i is 1,2, …, L + m-1m is less than or equal to L-2, U0(i) Defined as the mean value:
Figure RE-GDA0002610664430000044
vector quantity
Figure RE-GDA0002610664430000045
And
Figure RE-GDA0002610664430000046
the distance between
Figure RE-GDA0002610664430000047
Defined as the maximum difference between the corresponding elements.
Figure RE-GDA0002610664430000048
In the step S6, fuzzy membership functions are adopted
Figure RE-GDA0002610664430000049
Redefining
Figure RE-GDA00026106644300000410
And
Figure RE-GDA00026106644300000411
distance between, is recorded as
Figure RE-GDA00026106644300000412
Figure RE-GDA00026106644300000413
In this expression, the fuzzy function
Figure RE-GDA00026106644300000414
Is an exponential function. n and w are the width and gradient of the exponential function, respectively.
In the step S7, a function is defined
Figure RE-GDA00026106644300000415
Changing the reconstruction dimension from m to m +1, and repeating the steps (4) to (7). A set of m + 1-dimensional vectors is generated. Defining functions
Figure RE-GDA0002610664430000051
The fuzzy function for a given sequence U is defined by an equation
Figure RE-GDA0002610664430000052
When the length L of the sequence U is finite, the corresponding fuzzy function value is
FuzzyEn(m,n,r,N)＝lnφm(n,r)-lnφm+1(n,r)
Where m is the dimension of the phase space and r is the similarity tolerance.
In summary, the multi-scale permutation fuzzy entropy is:
Figure RE-GDA0002610664430000053
wherein the parameters are selected as follows: m is 1, n is 2, r is 0.25, pm is 4, and τ is 1.
Test examples
As shown in fig. 2-3, simulated fMRI data with 900 time points was generated using the SimTB tool box, adding gaussian white noise at 20% and 40% signal-to-noise intensities, respectively, in the simulated signal. Calculating the multi-scale permutation fuzzy entropy, performing statistical analysis, and comparing the entropy value and the p value change under 1-5 scales. The multiscale permutation fuzzy entropy was calculated for the collected fMRI data (HCP dataset, 900 time points) and the stability was tested using the re-confidence algorithm. Brain regions associated with advanced cognition were observed with a retest confidence level of greater than 0.4 at 1-5 scale.

Claims (8)

1. The functional magnetic resonance complexity measuring method based on the multi-scale permutation fuzzy entropy is characterized by comprising the following steps of:
step S1: acquiring resting state functional magnetic resonance image data, and preprocessing the image data;
step S2: performing low-pass filtering on the preprocessed data by using a Butterworth low-pass filter to obtain an original time sequence x (i) with the length of N;
step S3: data downsampling an original time series x (i), averaging the time series in an overlapping window of length s to construct a continuous coarse-grained time series
Figure FDA0002527116720000011
Step S4: reconstructing coarse-grained time series
Figure FDA0002527116720000012
Obtaining a matrix, arranging each reconstruction assembly in the matrix according to an ascending order, and performing symbolization to obtain a symbol sequence U (i);
step S5: performing phase space reconstruction on the symbol sequence u (i), specifically including:
assuming that U (i) has a length L, structure Yi m＝{U(i),U(i+1),…,U(i+m-1)}-U0(i)；
Wherein i is 1,2, …, L + m-1m is less than or equal to L-2, m is a phase space dimension,
Figure FDA0002527116720000013
vector Yi mAnd Yj mThe distance between
Figure FDA0002527116720000014
Defined as the maximum difference between the corresponding elements;
Figure FDA0002527116720000015
step S6: using fuzzy membership functions
Figure FDA0002527116720000016
Redefining Yi mAnd Yj mThe distance between them; wherein the fuzzy membership function
Figure FDA0002527116720000017
Is an exponential function, n represents the width of the exponential function, and w represents the gradient of the exponential function;
step S7: and calculating a multi-scale permutation fuzzy entropy value.
2. The method for measuring according to claim 1, wherein in step S1, the preprocessing of the image data comprises: and performing time-layer correction on the image data by adopting spm 8 and dparsf, correcting head movement, normalizing the functional image space into an MNI template, and performing linear trend removal and time-domain band-pass filtering.
3. The method of measurement according to claim 1, characterized in that in step S2 the amplitude of the butterworth low-pass filter frequency response is
Figure FDA0002527116720000018
Where t is the filter order, fcIs the cut-off frequency.
4. The method for measuring according to claim 3, wherein in step S3, x (i) ═ x is applied to the original time series of length N1,x2,…,xNCarry out data down-sampling with scale factor s to obtain kth coarse-grained time sequence
Figure FDA0002527116720000021
Is defined as:
Figure FDA0002527116720000022
wherein, s is a scale factor,
Figure FDA0002527116720000023
for each time series length, kth refers to the kth time series generated by overlapping windows; when s is 1, the coarse-grained time series is the original time series.
5. The method for measuring according to claim 4, wherein in step S4, coarse-grained time series are processed
Figure FDA0002527116720000024
The matrix obtained by reconstruction is:
Figure FDA0002527116720000025
where τ is the embedding time delay, pm is the permutation dimension,
Figure FDA0002527116720000026
each row in the matrix is a reconstruction component, and the matrix comprises K reconstruction components.
6. The method for measuring according to claim 5, characterized in that in step S4, each reconstructed component in the matrix is arranged in ascending order and symbolized:
index extraction is carried out on all elements of the reconstruction assembly in the matrix to obtain a symbol sequence, wherein each pm! The symbol sequence corresponds to 1 to pm! A value of (d);
rearranging all elements in each reconstruction component in ascending order;
if the two element values are equal, the next element value of the corresponding reconstruction component is used as the current comparison result, and the instantaneous change trend of the time sequence is reflected by rearrangement;
if the next element value is still equal, the index value is used for carrying out ascending rearrangement;
after ascending rearrangement, coarse-grained time series
Figure FDA0002527116720000027
Conversion to have between 1 and pm with each element! A sequence of values between
Figure FDA0002527116720000031
7. The method for measuring according to claim 6, wherein in step S6, fuzzy membership functions are used
Figure FDA0002527116720000032
Redefining Yi mAnd Yj mDistance between, is recorded as
Figure FDA0002527116720000033
Figure FDA0002527116720000034
Wherein the fuzzy membership function
Figure FDA0002527116720000035
For an exponential function, n represents the width of the exponential function and w represents the gradient of the exponential function.
8. The method for measuring according to claim 7, characterized in that, in step S7,
defining a function:
Figure FDA0002527116720000036
changing the reconstructed phase space dimension from m to m +1, and repeating the steps S4 to S7 to generate a group of vectors with m +1 dimensions;
defining a function:
Figure FDA0002527116720000037
the fuzzy function for a given sequence u (i) is defined by the equation:
Figure FDA0002527116720000038
when the length L of the sequence U (i) is finite, the fuzzy function value is
FuzzyEn(m,n,r,N)＝lnφm(n,r)-lnφm+1(n,r)
Wherein m is the phase space dimension and r is the similarity tolerance;
in summary, the multi-scale permutation fuzzy entropy is:
Figure FDA0002527116720000041
wherein the parameters are selected as follows: m is 1, n is 2, r is 0.25, pm is 4, and τ is 1.
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